President's Messages: Linda M. Gojak
Linda M. Gojak
Twenty-five years ago NCTM released Curriculum and Evaluation Standards for Teaching Mathematics, which presented a comprehensive vision for mathematics teaching, learning, and assessment in grades K–12. Other significant publications, including Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics continue to identify what we believe students should know and be able to do throughout their school mathematics experience. Since this is my final President’s Message, I thought this would be a good time to look at what the mathematics education community has accomplished since 1989 and the challenges that we must continue to address.
One of the highlights of my work as president has been meeting teachers of mathematics in kindergarten through college from all around the country. It is immediately obvious that they care deeply about their students. It is also evident that in this era of high-stakes tests, teachers are worried about how decisions made by elected officials will affect their ability to do what is best for students and their own futures. The role of classroom teachers and other educators must include advocating to decision makers on behalf of their students, themselves, and their schools.
This February is a month of recognizing accomplishments and achievements including the Super Bowl and the Winter Olympics. So what does this have to do with teaching mathematics? Much has been written on the psychology of playing not to lose vs. playing to win. Although the context for this work is usually sports or success in the business world, I am intrigued about the psychology of playing to win as I think about its implications for teaching mathematics.
I have a colleague who entered teaching after many years in another profession. She teaches middle school mathematics in an urban setting. She has spent her teaching career in the same school and has witnessed many changes in the community. Having had many opportunities to collaborate with her, I both admire and envy the professionalism that she brings to her classroom and her colleagues.
One of the questions I am asked frequently by teachers, parents, and reporters is, “When should students take algebra?” Let’s assume that we’re talking about a college preparatory algebra 1 course. The content and instruction must be designed to develop both conceptual and procedural understanding. For students to be considered successful in first-year algebra, the expectation must be that reasoning and making sense will be priorities of both teaching and learning.
I worry about the instructional time we lose when we spend so much time on testing. I worry about the pressure we put on students when so much of their time in schools is spent being tested. I worry that we have taken the joy out of teaching and learning in the name of accountability that can be determined “only” by giving more tests.
Too often when a student struggles with mathematics, a parent comments, “I was never very good at math either.” While that may be true, the need for our students to be successful in mathematics is more urgent than at any time in recent history. In this era of focus on college, career, and life readiness, engaging parents is critical to the success of students from prekindergarten through high school.
We are currently on a journey that has the potential to make an unprecedented difference for students if we think purposefully about how to change practice and about the content that we teach. Teachers are only one part of the “we” necessary to realize the potential of the Common Core. “We” also includes pre-K–16 educators, administrators, parents, state and national governmental agencies, legislators, policymakers, and the business community.
Linda M. Gojak
Summer is here! Time for picnics, playing at the beach, gardening, and reading! One of my fondest memories as an elementary student was riding my bike to the pool and stopping at the library on the way home to pick up another book for the summer reading club. At the end of each school year, we were given a summer reading list with two books assigned and the others as suggested readings. I still love to read and summer is the time to enjoy the books that have been sitting on my shelf waiting to spend some time with me.
Early in my career, the principal of my school shared The Animal School: A Fable, written in the 1940s by George Reavis, assistant superintendent of Cincinnati Public Schools. At the time I was teaching in a fifth-grade self-contained classroom in a K–5 school. That story made a deep impression on me and strongly influenced how I thought about my students—their talents and interests.
Since the release of the Common Core State Standards for Mathematics (CCSSM) nearly three years ago, I have thought long and hard about them. I have considered the standards from the viewpoint of state leaders helping districts to make the transition from previous standards to the Common Core. I have examined the standards closely by asking questions of the CCSSM authors. I have spent time in schools talking with teachers. I have worked at the district level with the elementary teachers and coaches who are preparing to implement the standards. The focus on effective mathematics instruction and efforts to improve it at all levels speak to the potential impact of the Common Core.
Have you ever spent time carefully planning a lesson only to find your students totally unreceptive? Several years ago, I participated in an outstanding problem-solving seminar and returned to my class eager to put many of the new ideas into practice. Despite my enthusiasm, my students rebelled! Why weren’t my students as excited about this as I was? Was it because they couldn’t solve the problem quickly that they gave up with loud moans of protest?
Recently, I had a conversation with a group of math coaches who are working with elementary teachers on implementation of the Common Core Standards for Mathematics. The discussion turned to a description of rigor in the classroom. The coaches commented that many of their teachers were confused by exactly what was meant by teaching and learning with rigor. The coaches weren’t sure how to respond.
How often do our students consider their mistakes to be signs of failure? How many students, as well as parents, believe that the goal of learning mathematics is solely to get the correct answer? How often, on arriving at an answer, do students believe their thinking about the problem is finished? In The Phantom Tollbooth, author Norton Juster offers a valuable contrasting perspective.
There is a tale from the Middle Ages about a magic pebble, called the touchstone, that when rubbed against any metal, would turn the metal into gold. It was said that this pebble could be found on the shores of the Black Sea. It looked like any other pebble on the beach. The only difference between the touchstone and the other pebbles was that it was warm to the touch, and all the others felt cold.
As mathematics educators at all levels consider effective implementation and instruction related to state or Common Core standards, a frequently asked question is, “What does it mean to be fluent in mathematics?” The answer, more often than not, is, “Fast and accurate.” Building fluency should involve more than speed and accuracy. It must reach beyond procedures and computation.
Over the last three decades a variety of instructional strategies have been introduced with a goal of increasing student achievement in mathematics. Such strategies include individualized instruction, cooperative learning, direct instruction, inquiry, scaffolding, computer-assisted instruction, and problem solving. A recent strategy receiving much attention is the “flipped classroom.”
Since developing its bold Agenda for Action in 1980, NCTM has provided mathematics educators with several groundbreaking publications that have defined a vision for change in mathematics education. Although mathematical content is important in all of these publications, they also focus on the significance of changing traditional approaches to teaching mathematics—change that is critical to offering every child the opportunity to achieve his or her maximum potential in mathematics.
The month of August is a special time for teachers and students. Teachers are preparing classrooms and materials, eagerly awaiting the opening of school. Students are buying school supplies and clothes. Both are likely to be dreading the end of summer vacation but also excited about going back to school. This is a season of anticipation—new teachers, new students, new materials, new ideas—even new pencils. It is an exciting time for everyone. Unlike any other career, teaching offers us a chance for a new beginning—a fresh start!